It is an open problem to determine whether a polygonal chain can be
“straightened” in the plane if its links are not allowed to cross.
This problem has been raised independently by several researchers, including
J. Mitchell, and W. Lenhart and S. Whitesides [LW95]. In this paper, we
propose a related question: whether a tree linkage can always be
“straightened” in the plane, without allowing its links to cross.
We prove that this is not always possible.